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Nonlinear and Mixed Integer Linear Programming
2012In this chapter we compare continuous nonlinear optimization with mixed integer optimization of water supply networks by means of a meso scaled network instance. We introduce a heuristic approach, which handles discrete decisions arising in water supply network optimization through penalization using nonlinear programming.
Kolb, Oliver +3 more
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Safe bounds in linear and mixed-integer linear programming
Mathematical Programming, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Arnold Neumaier, Oleg Shcherbina
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Mixed-Integer Linear Programming Formulations
2014In this chapter, (mixed-)integer linear programming formulations of the resource-constrained project scheduling problem are presented. Standard formulations from the literature and newly proposed formulations are classified according to their size in function of the input data.
Artigues, Christian +3 more
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An optimality cut for mixed integer linear programs
European Journal of Operational Research, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gilbert Laporte, Frédéric Semet
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The Mixed Integer Linear Bilevel Programming Problem
Operations Research, 1990A two-person, noncooperative game in which the players move in sequence can be modeled as a bilevel optimization problem. In this paper, we examine the case where each player tries to maximize the individual objective function over a jointly constrained polyhedron. The decision variables are variously partitioned into continuous and discrete sets. The
James T. Moore, Jonathan F. Bard
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A DC Programming Approach for Mixed-Integer Linear Programs
2008In this paper, we propose a new efficient algorithm for globally solving a class of Mixed Integer Program (MIP). If the objective function is linear with both continuous variables and integer variables, then the problem is called a Mixed Integer Linear Program (MILP). Researches on MILP are important in both theoretical and practical aspects.
Yi-Shuai Niu, Pham Dinh Tao
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From Mixed-Integer Linear to Mixed-Integer Bilevel Linear Programming
2017Bilevel Optimization is a very challenging framework where two players (with different objectives) compete for the definition of the final solution. In this paper we address a generic mixed-integer bilevel linear program, i.e., a bilevel optimization problem where the objective functions and constraints are all linear, and some variables are required ...
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Bivium as a Mixed-Integer Linear Programming Problem
2009Trivium is a stream cipher proposed for the eSTREAM project. Raddum introduced some reduced versions of Trivium, named Bivium A and Bivium B. In this article we present a numerical attack on the Biviums. The main idea is to transform the problem of solving a sparse system of quadratic equations over GF (2) into a combinatorial optimization problem.
Julia Borghoff +2 more
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Marginal values in mixed integer linear programming
Mathematical Programming, 1989Marginal values of a given optimization problem are the directional partial derivatives of the value with respect to perturbations in the data. If \(v(c,A,b)=\min \{cx|\) Ax\(\geq b\), \(x\geq 0\}\) and if \(u=(c',A',b')\) is a vector, then the marginal value in direction u is defined by \[ \frac{\partial v}{\partial u}=\lim_{\epsilon \to 0+}\frac{v(c+\
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Linear and Mixed Integer Programming
2000Linear Programming (LP) is one of the most famous optimization techniques introduced independently by Kantarowitsch in 1939 and by Dantzig in 1949 (Kreko, 1973). LP is applicable in decision situations where quantities (variables) can take any real values only restricted by linear (in-) equalities, e. g. for representing capacity constraints. Still, LP
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